Suspension Bridges (Hänge- und Spannbandbrücken) 12.05.2020 ETH Zürich | Chair of Concrete Structures and Bridge Design | Bridge Design 1
Common aspects Suspension bridges Overview Suspension bridges (types of suspension bridges) Cable system Stiffening girder Towers stress-ribbons Anchor blocks (suspended bridges) Cable-stayed bridges 12.05.2020 ETH Zürich | Chair of Concrete Structures and Bridge Design | Bridge Design 2
Suspension Bridges Overview 12.05.2020 ETH Zürich | Chair of Concrete Structures and Bridge Design | Bridge Design 3
Suspension Bridges – Overview • Suspension bridge Bridges carrying loads primarily by funicular action of (Hängebrücke) cables can be categorised as follows: → Suspension bridges: Strongly sagging main cables main cables spanning between towers. Cables loaded laterally by vertical hangers connecting the suspended hangers / suspender cables deck girder to the main cables. → Suspended bridges / stress-ribbons: Slightly sagging main cables, spanning between anchor block tower / pylon deck / abutments without towers. Cables loaded laterally stiffening girder by the deck girder. The deck follows the cable profile in elevation. scale differs by an order of magnitude • Suspended bridges are commonly referred to as stress-ribbons if the deck consists of a prestressed concrete slab. However, the term “stress - ribbon” is also used for other types of suspended bridges. Suspended bridge / Stress-ribbon (Spannband) • The typical spans of suspension bridges and suspended bridges / stress-ribbons differ by an order of magnitude. 12.05.2020 ETH Zürich | Chair of Concrete Structures and Bridge Design | Bridge Design 4
Suspension Bridges – Overview • Suspended bridges without any stiffening girder were presumably among the first bridges mankind used. • The stiffness of such bridges essentially corresponds to that of the main cables: → very flexible structures under non-funicular loads (see section static analysis of cables ) → range of application very limited: Trails, pedestrian bridges with alternative routes (wheelchairs), etc. • Suspended bridges are very efficient, and can be designed and built with moderate technical know-how unless spans are very long (such as in the Randa bridge designed by Theo Lauber, with a span of 494 m, equipped with special damping devices). • Such bridges have recently gained popularity in Switzerland, partly for access in mountain areas, partly as mere tourist attractions. • Many of these bridges are designed following design guidelines established by Helvetas more than 50 years ago, see next slide. 12.05.2020 ETH Zürich | Chair of Concrete Structures and Bridge Design | Bridge Design 5
Suspension Bridges – Overview • Helvetas launched first projects for erecting trail bridges in Nepal in 1956. Since then, more than 7’000 trail bridges have been built, with suspended bridges up to spans of 156 m, and suspension bridges up to 355 m (see notes for details). • Today, activities range from advising the government on its vocational training and trail bridge programs to practical activities reducing communities' vulnerability to disasters. • For more information on the Helvetas trail bridge programme see www.helvetas.org. 12.05.2020 ETH Zürich | Chair of Concrete Structures and Bridge Design | Bridge Design 6
Suspension Bridges – Overview • The span range of suspended bridges is limited, among other reasons by aerodynamic stability (overturning of “deck”, as e.g. occurred in the first Trift trail bridge in Switzerland). • For longer spans, suspension footbridges are used, both in Nepal and in Switzerland. Some of them are spectacular, such as the Panoramabrücke Sigriswil with a span of 344 m, 85 m above ground (Martin Dietrich, Theiler Ingenieure). 12.05.2020 ETH Zürich | Chair of Concrete Structures and Bridge Design | Bridge Design 7
Suspension Bridges – Overview • The focus of the lecture is, however, on suspension bridges carrying road and/or rail traffic (upper photo). • Some peculiarities of stress-ribbon bridges are also discussed (lower photo). • Suspended bridges and suspension footbridges are not treated in more detail in the lecture. 12.05.2020 ETH Zürich | Chair of Concrete Structures and Bridge Design | Bridge Design 8
Suspension Bridges Cable system 12.05.2020 ETH Zürich | Chair of Concrete Structures and Bridge Design | Bridge Design 9
Suspension Bridges – Cable system • Many cable layouts are possible, whose suitability depends on Earth-anchored the specific site. Preferences of clients and designers are also without important due to the high visual impact of long-span bridges. girder side spans simply • The figure schematically shows a selection of common solutions, supported side spans which differ mainly in the following aspects: suspended • Anchorage: Earth- or self-anchored • Side span length and support: Suspended, on piers or none side spans • Girder continuity: Simply supported or continuous on piers • In all these solutions, cable planes are commonly vertical side spans (construction process!) and common sag/span ratios range from suspended 1/8 … 1/11, with the following advantages of large/small sag: • large sag side spans → lower cable forces = savings in cables and anchorages girder suspended continuous • small sag → stiffer cables = reduced deck girder bending moments, Self-anchored better aerodynamic behaviour → shorter towers and more elegant appearance side spans on piers • The most economical sag/span ratio would be larger (about 1/6, see Gimsing 2012), but deflections under traffic loads are side spans excessive at such large sags (see static analysis of cables ). suspended 12.05.2020 ETH Zürich | Chair of Concrete Structures and Bridge Design | Bridge Design 10
Suspension Bridges Cable system Preliminary cable dimensions 12.05.2020 ETH Zürich | Chair of Concrete Structures and Bridge Design | Bridge Design 11
Suspension Bridges – Cable system: Preliminary cable dimensions • In preliminary design, the main cable dimensions may be estimated Estimation of suspension cable force (parabolic sag) based on a parabolic cable geometry and the dead load sag : ( ) ( ) + + + + + Q 2 2 g g q l g g q l 2 Q Ql = + = m m H q 8 f 4 f 8 f g + + 4 f 2 2 2 2 l 16 f l 16 f ( ) = + + + H l T H g g q l 2 Q m l 8 f f H • In the above equation, the main cable dead load g m must first be estimated, requiring iteration. Knowing the cable strength f sd and its l specific weight g m (total cable weight per length / steel cross- sectional area), the equation can be solved for the required steel Estimation of hanger forces area A m : ( ) + + + [Gimsing 2012] 2 2 g q l 2 Q l 16 f = = g → T A f , g A A F m sd m m m m − g + h 2 2 8 f f l l 16 f sd m Q The required hanger cross-section can be estimated by attributing to each hanger the uniformly distributed load (including traffic loads) q corresponding to its part of the deck surface, assuming that g concentrated loads are distributed over a length of 30d: d Q T = + + → h T g q s A h h h 30 d f sd s h s h s h s h 12.05.2020 ETH Zürich | Chair of Concrete Structures and Bridge Design | Bridge Design 12
Suspension Bridges Cable system Earth anchored vs. self-anchored 12.05.2020 ETH Zürich | Chair of Concrete Structures and Bridge Design | Bridge Design 13
Suspension Bridges – Cable system: Earth-anchored vs. self-anchored • Conventional suspension bridges are earth-anchored Earth-anchored • suspension cables are fixed to anchor blocks at their ends without girder side spans • stiffening girder carries no substantial axial force simply supported • However, suspension bridges can also be self-anchored, just like side spans cable-stayed bridges where this is the common solution: suspended • suspension cables transfer the horizontal component of the cable force to the stiffening girder at their ends side spans on piers • stiffening girder carries compressive force of equal magnitude as the horizontal component of the cable force side spans • Self-anchored suspension bridges have the following suspended advantages and drawbacks: • no need for anchor blocks (commonly heavy and expensive) side spans girder suspended • larger cross-section of stiffening girder required continuous • complicated erection (suspension cables can carry loads only Self-anchored after stiffening girder is continuous, similar as in tied arches) side spans • The latter is a severe limitation, and hence, though the system on piers was popular e.g. in Germany during the first decades of the 20 th century, only few major self-anchored suspension bridges have side spans been built, all of them with moderate spans. suspended 12.05.2020 ETH Zürich | Chair of Concrete Structures and Bridge Design | Bridge Design 14
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